Partial

One note contains many notes

The page Klang-Spektrum introduces it like this: if a flute plays the A above middle C and a violin the same note, both vibrate 440 times per second, the pitch is identical. Nevertheless you can hear after a few tenths of a second which instrument is playing. The difference lies in what sounds along above it. A vibrating string or column of air never vibrates only as a whole, but at the same time in halves, thirds, quarters. The half sounds with twice the frequency, the third with three times. These notes are called partials; from the second partial onwards one also speaks of overtones.

With a fundamental of 110 Hz they lie, according to the page, at 220, 330, 440, 550, 660 Hz and so on. Musically remarkable: the second partial lies an octave above the fundamental, the third a fifth above that, the fourth an octave again, the fifth a major third. The major triad is therefore physically contained in every single note. According to the page this is no accident of Western music but a property of vibrating bodies.

The spectrum as timbre

A sound spectrum shows the partials as bars: horizontally the frequency, vertically the strength. The left bar is the fundamental. The pitch is in the distance of the bars, the timbre in their heights. The flute has a strikingly poor spectrum: the fundamental dominates, the second partial lies at about a fifth of its strength, everything above almost vanishes. It therefore sounds soft, round and a little hollow. The violin has a dense spectrum: the fifth partial is still half as strong as the fundamental, the eighth clearly audible. That gives it the brilliant and cutting quality. The page Building block: timbre puts it like this: this very mixing ratio is what our ear perceives as “colour”.

To try out

The Klang-Spektrum page describes two experiments. On the piano you silently depress the chord C3–G3–C4–E4 in the treble, hold the keys down and then strike the low C2 firmly. After you let go, the silently held strings go on sounding; they have been set vibrating by the overtones of the struck note.

On the guitar the same works through harmonics: a finger that only touches the string above the twelfth fret forces a vibration node in the middle and lets the second partial sound. Above the seventh fret the third partial comes, above the fifth the fourth. The fret positions are directly readable divisions of the string: 1/2, 1/3, 1/4.

Common mistakes

• Equating overtone and partial: The first partial is the fundamental, the first overtone is the second partial.
• Taking partials for properties of single instruments: They are in every note of a vibrating body, only their strengths differ.
• Fretting the harmonic firmly: You touch the string only lightly.